Mr. Koger is making copies of the school literary magazine to distribute to students and faculty. He has access to two copy machines: an older machine and a new machine. If he used only the older machine, it would take 80 minutes longer than if he used only the new machine. If he used both machines, he would finish the job in 30 minutes. When m is the number of minutes it would take to finish the job using only the new machine, the situation is modeled by this rational equation: . How many minutes would it take to finish the job if Mr. Koger used only the new machine?

Two streets intersect at a 30- degree angle. at the intersection, the are four crosswalks formed that are the same length. what type of quadrilateral is formed by the crosswalks?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Read the excerpt from the strange case of dr jekyll and mr. hyde what do dr. jekyll's thoughts reveal about him in this excerpt? [t]he inmates of my house were locked in the most rigorous hours of slumber, and i determined, flushed as i was with hope and triumph, to venture in my new shape as far as to my bedroom. i crossed the yard, wherein the constellations looked down upon me, i could have thought, with wonder, the first creature of that sort that their unsleeping vigilance had yet disclosed to he is jealous of those who can sleep through the night. he is revered for his scientific advances. he is interested in studying the movements of the stars he is proud and enthusiastic about his initial results.